Test on Iceberg code

[bachase]

Test the fault tolerance of circuit gadgets in https://www.nature.com/articles/s41534-018-0085-z

[Misty-W]

Hi @bachase, I've worked out a potential solution for generating the operators for the iceberg and the quantum Hamming code, following the structure of surface_code.py and using code constructions from the qldpc library.
I've held off submitting a PR until I resolve some problems with installing Bitwuzla and test it properly, hopefully soon.

[Misty-W]

I should clarify that the circuit gadgets to test from Fault-tolerant quantum computation with few qubits
are those encoded by the quantum Hamming [15, 7, 3] code rather than the iceberg code. The iceberg code is an error detection code, whereas the quantum Hamming code is an error correction code.

In Fault-tolerant quantum computation with few qubits, "fault tolerance for a distance-two code means that any single fault within an operation should either have no effect or lead to a detectable error," which is why they can use an error detection code to make claims about "fault tolerant" circuit gadgets.

On the other hand, in the FT checker paper, "the gadget is fault tolerant if and only if each symbolic configuration in cfgs describes a set of noisy states that are not 'too far' from the error-free output state," which requires error correction.

That said, the iceberg code could still be useful for the FT checker if #14 or a similar issue expands the supported definitions to include that in Fault-tolerant quantum computation with few qubits.